Properties

Label 4900.2.a.bi.1.1
Level $4900$
Weight $2$
Character 4900.1
Self dual yes
Analytic conductor $39.127$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4900,2,Mod(1,4900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4900, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4900.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4900.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(39.1266969904\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 6x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.28825\) of defining polynomial
Character \(\chi\) \(=\) 4900.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.28825 q^{3} +2.23607 q^{9} +O(q^{10})\) \(q-2.28825 q^{3} +2.23607 q^{9} -5.47214 q^{11} +0.874032 q^{13} -4.57649 q^{17} -5.99070 q^{19} -3.47214 q^{23} +1.74806 q^{27} +0.236068 q^{29} -8.27895 q^{31} +12.5216 q^{33} +4.23607 q^{37} -2.00000 q^{39} -5.11667 q^{41} +3.76393 q^{43} -4.91034 q^{47} +10.4721 q^{51} +11.7082 q^{53} +13.7082 q^{57} +1.95440 q^{59} -7.53244 q^{61} -13.9443 q^{67} +7.94510 q^{69} +16.7082 q^{71} +7.53244 q^{73} -11.4721 q^{79} -10.7082 q^{81} -12.1877 q^{83} -0.540182 q^{87} -5.86319 q^{89} +18.9443 q^{93} -16.3516 q^{97} -12.2361 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{11} + 4 q^{23} - 8 q^{29} + 8 q^{37} - 8 q^{39} + 24 q^{43} + 24 q^{51} + 20 q^{53} + 28 q^{57} - 20 q^{67} + 40 q^{71} - 28 q^{79} - 16 q^{81} + 40 q^{93} - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.28825 −1.32112 −0.660560 0.750774i \(-0.729681\pi\)
−0.660560 + 0.750774i \(0.729681\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 2.23607 0.745356
\(10\) 0 0
\(11\) −5.47214 −1.64991 −0.824956 0.565198i \(-0.808800\pi\)
−0.824956 + 0.565198i \(0.808800\pi\)
\(12\) 0 0
\(13\) 0.874032 0.242413 0.121206 0.992627i \(-0.461324\pi\)
0.121206 + 0.992627i \(0.461324\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.57649 −1.10996 −0.554981 0.831863i \(-0.687275\pi\)
−0.554981 + 0.831863i \(0.687275\pi\)
\(18\) 0 0
\(19\) −5.99070 −1.37436 −0.687181 0.726486i \(-0.741152\pi\)
−0.687181 + 0.726486i \(0.741152\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.47214 −0.723990 −0.361995 0.932180i \(-0.617904\pi\)
−0.361995 + 0.932180i \(0.617904\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.74806 0.336415
\(28\) 0 0
\(29\) 0.236068 0.0438367 0.0219184 0.999760i \(-0.493023\pi\)
0.0219184 + 0.999760i \(0.493023\pi\)
\(30\) 0 0
\(31\) −8.27895 −1.48694 −0.743472 0.668767i \(-0.766822\pi\)
−0.743472 + 0.668767i \(0.766822\pi\)
\(32\) 0 0
\(33\) 12.5216 2.17973
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.23607 0.696405 0.348203 0.937419i \(-0.386792\pi\)
0.348203 + 0.937419i \(0.386792\pi\)
\(38\) 0 0
\(39\) −2.00000 −0.320256
\(40\) 0 0
\(41\) −5.11667 −0.799090 −0.399545 0.916714i \(-0.630832\pi\)
−0.399545 + 0.916714i \(0.630832\pi\)
\(42\) 0 0
\(43\) 3.76393 0.573994 0.286997 0.957931i \(-0.407343\pi\)
0.286997 + 0.957931i \(0.407343\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.91034 −0.716247 −0.358123 0.933674i \(-0.616583\pi\)
−0.358123 + 0.933674i \(0.616583\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 10.4721 1.46639
\(52\) 0 0
\(53\) 11.7082 1.60825 0.804123 0.594463i \(-0.202635\pi\)
0.804123 + 0.594463i \(0.202635\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 13.7082 1.81570
\(58\) 0 0
\(59\) 1.95440 0.254441 0.127220 0.991874i \(-0.459394\pi\)
0.127220 + 0.991874i \(0.459394\pi\)
\(60\) 0 0
\(61\) −7.53244 −0.964430 −0.482215 0.876053i \(-0.660168\pi\)
−0.482215 + 0.876053i \(0.660168\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −13.9443 −1.70356 −0.851782 0.523896i \(-0.824478\pi\)
−0.851782 + 0.523896i \(0.824478\pi\)
\(68\) 0 0
\(69\) 7.94510 0.956478
\(70\) 0 0
\(71\) 16.7082 1.98290 0.991449 0.130491i \(-0.0416554\pi\)
0.991449 + 0.130491i \(0.0416554\pi\)
\(72\) 0 0
\(73\) 7.53244 0.881605 0.440803 0.897604i \(-0.354694\pi\)
0.440803 + 0.897604i \(0.354694\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −11.4721 −1.29072 −0.645358 0.763880i \(-0.723292\pi\)
−0.645358 + 0.763880i \(0.723292\pi\)
\(80\) 0 0
\(81\) −10.7082 −1.18980
\(82\) 0 0
\(83\) −12.1877 −1.33778 −0.668889 0.743362i \(-0.733230\pi\)
−0.668889 + 0.743362i \(0.733230\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.540182 −0.0579135
\(88\) 0 0
\(89\) −5.86319 −0.621496 −0.310748 0.950492i \(-0.600580\pi\)
−0.310748 + 0.950492i \(0.600580\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 18.9443 1.96443
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −16.3516 −1.66025 −0.830125 0.557577i \(-0.811731\pi\)
−0.830125 + 0.557577i \(0.811731\pi\)
\(98\) 0 0
\(99\) −12.2361 −1.22977
\(100\) 0 0
\(101\) −3.36861 −0.335189 −0.167595 0.985856i \(-0.553600\pi\)
−0.167595 + 0.985856i \(0.553600\pi\)
\(102\) 0 0
\(103\) 18.3848 1.81151 0.905753 0.423806i \(-0.139306\pi\)
0.905753 + 0.423806i \(0.139306\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.4721 1.20573 0.602863 0.797844i \(-0.294026\pi\)
0.602863 + 0.797844i \(0.294026\pi\)
\(108\) 0 0
\(109\) −16.4164 −1.57241 −0.786203 0.617968i \(-0.787956\pi\)
−0.786203 + 0.617968i \(0.787956\pi\)
\(110\) 0 0
\(111\) −9.69316 −0.920034
\(112\) 0 0
\(113\) 13.7639 1.29480 0.647401 0.762150i \(-0.275856\pi\)
0.647401 + 0.762150i \(0.275856\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.95440 0.180684
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 18.9443 1.72221
\(122\) 0 0
\(123\) 11.7082 1.05569
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −11.1803 −0.992095 −0.496047 0.868295i \(-0.665216\pi\)
−0.496047 + 0.868295i \(0.665216\pi\)
\(128\) 0 0
\(129\) −8.61280 −0.758315
\(130\) 0 0
\(131\) 2.16073 0.188784 0.0943918 0.995535i \(-0.469909\pi\)
0.0943918 + 0.995535i \(0.469909\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 10.0000 0.854358 0.427179 0.904167i \(-0.359507\pi\)
0.427179 + 0.904167i \(0.359507\pi\)
\(138\) 0 0
\(139\) −10.3609 −0.878797 −0.439399 0.898292i \(-0.644808\pi\)
−0.439399 + 0.898292i \(0.644808\pi\)
\(140\) 0 0
\(141\) 11.2361 0.946248
\(142\) 0 0
\(143\) −4.78282 −0.399960
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 6.70820 0.549557 0.274779 0.961507i \(-0.411395\pi\)
0.274779 + 0.961507i \(0.411395\pi\)
\(150\) 0 0
\(151\) 8.23607 0.670242 0.335121 0.942175i \(-0.391223\pi\)
0.335121 + 0.942175i \(0.391223\pi\)
\(152\) 0 0
\(153\) −10.2333 −0.827317
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −9.02546 −0.720310 −0.360155 0.932892i \(-0.617276\pi\)
−0.360155 + 0.932892i \(0.617276\pi\)
\(158\) 0 0
\(159\) −26.7912 −2.12468
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −2.18034 −0.170777 −0.0853887 0.996348i \(-0.527213\pi\)
−0.0853887 + 0.996348i \(0.527213\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4.11512 −0.318438 −0.159219 0.987243i \(-0.550898\pi\)
−0.159219 + 0.987243i \(0.550898\pi\)
\(168\) 0 0
\(169\) −12.2361 −0.941236
\(170\) 0 0
\(171\) −13.3956 −1.02439
\(172\) 0 0
\(173\) 18.3848 1.39777 0.698884 0.715235i \(-0.253680\pi\)
0.698884 + 0.715235i \(0.253680\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −4.47214 −0.336146
\(178\) 0 0
\(179\) 1.70820 0.127677 0.0638386 0.997960i \(-0.479666\pi\)
0.0638386 + 0.997960i \(0.479666\pi\)
\(180\) 0 0
\(181\) 3.62365 0.269344 0.134672 0.990890i \(-0.457002\pi\)
0.134672 + 0.990890i \(0.457002\pi\)
\(182\) 0 0
\(183\) 17.2361 1.27413
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 25.0432 1.83134
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −12.1803 −0.881338 −0.440669 0.897670i \(-0.645259\pi\)
−0.440669 + 0.897670i \(0.645259\pi\)
\(192\) 0 0
\(193\) −15.6525 −1.12669 −0.563345 0.826222i \(-0.690486\pi\)
−0.563345 + 0.826222i \(0.690486\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 19.4721 1.38733 0.693666 0.720297i \(-0.255994\pi\)
0.693666 + 0.720297i \(0.255994\pi\)
\(198\) 0 0
\(199\) 21.6746 1.53647 0.768235 0.640168i \(-0.221135\pi\)
0.768235 + 0.640168i \(0.221135\pi\)
\(200\) 0 0
\(201\) 31.9079 2.25061
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −7.76393 −0.539631
\(208\) 0 0
\(209\) 32.7820 2.26757
\(210\) 0 0
\(211\) 9.52786 0.655925 0.327963 0.944691i \(-0.393638\pi\)
0.327963 + 0.944691i \(0.393638\pi\)
\(212\) 0 0
\(213\) −38.2325 −2.61965
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −17.2361 −1.16471
\(220\) 0 0
\(221\) −4.00000 −0.269069
\(222\) 0 0
\(223\) −11.8539 −0.793795 −0.396898 0.917863i \(-0.629913\pi\)
−0.396898 + 0.917863i \(0.629913\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.40337 0.425006 0.212503 0.977160i \(-0.431838\pi\)
0.212503 + 0.977160i \(0.431838\pi\)
\(228\) 0 0
\(229\) 5.57804 0.368607 0.184304 0.982869i \(-0.440997\pi\)
0.184304 + 0.982869i \(0.440997\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 10.5279 0.689703 0.344852 0.938657i \(-0.387929\pi\)
0.344852 + 0.938657i \(0.387929\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 26.2511 1.70519
\(238\) 0 0
\(239\) 8.65248 0.559682 0.279841 0.960046i \(-0.409718\pi\)
0.279841 + 0.960046i \(0.409718\pi\)
\(240\) 0 0
\(241\) 1.41421 0.0910975 0.0455488 0.998962i \(-0.485496\pi\)
0.0455488 + 0.998962i \(0.485496\pi\)
\(242\) 0 0
\(243\) 19.2588 1.23545
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −5.23607 −0.333163
\(248\) 0 0
\(249\) 27.8885 1.76736
\(250\) 0 0
\(251\) −1.74806 −0.110337 −0.0551684 0.998477i \(-0.517570\pi\)
−0.0551684 + 0.998477i \(0.517570\pi\)
\(252\) 0 0
\(253\) 19.0000 1.19452
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −8.27895 −0.516427 −0.258213 0.966088i \(-0.583134\pi\)
−0.258213 + 0.966088i \(0.583134\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0.527864 0.0326740
\(262\) 0 0
\(263\) −10.7082 −0.660296 −0.330148 0.943929i \(-0.607099\pi\)
−0.330148 + 0.943929i \(0.607099\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 13.4164 0.821071
\(268\) 0 0
\(269\) 32.2418 1.96582 0.982908 0.184099i \(-0.0589367\pi\)
0.982908 + 0.184099i \(0.0589367\pi\)
\(270\) 0 0
\(271\) 24.8369 1.50873 0.754366 0.656454i \(-0.227945\pi\)
0.754366 + 0.656454i \(0.227945\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 20.9443 1.25842 0.629210 0.777236i \(-0.283379\pi\)
0.629210 + 0.777236i \(0.283379\pi\)
\(278\) 0 0
\(279\) −18.5123 −1.10830
\(280\) 0 0
\(281\) −24.1246 −1.43915 −0.719577 0.694413i \(-0.755664\pi\)
−0.719577 + 0.694413i \(0.755664\pi\)
\(282\) 0 0
\(283\) −10.5672 −0.628155 −0.314077 0.949397i \(-0.601695\pi\)
−0.314077 + 0.949397i \(0.601695\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 3.94427 0.232016
\(290\) 0 0
\(291\) 37.4164 2.19339
\(292\) 0 0
\(293\) 19.8477 1.15951 0.579757 0.814789i \(-0.303147\pi\)
0.579757 + 0.814789i \(0.303147\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −9.56564 −0.555055
\(298\) 0 0
\(299\) −3.03476 −0.175505
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 7.70820 0.442825
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −18.7186 −1.06833 −0.534164 0.845381i \(-0.679374\pi\)
−0.534164 + 0.845381i \(0.679374\pi\)
\(308\) 0 0
\(309\) −42.0689 −2.39322
\(310\) 0 0
\(311\) 9.40802 0.533480 0.266740 0.963769i \(-0.414054\pi\)
0.266740 + 0.963769i \(0.414054\pi\)
\(312\) 0 0
\(313\) 3.57494 0.202068 0.101034 0.994883i \(-0.467785\pi\)
0.101034 + 0.994883i \(0.467785\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −0.416408 −0.0233878 −0.0116939 0.999932i \(-0.503722\pi\)
−0.0116939 + 0.999932i \(0.503722\pi\)
\(318\) 0 0
\(319\) −1.29180 −0.0723267
\(320\) 0 0
\(321\) −28.5393 −1.59291
\(322\) 0 0
\(323\) 27.4164 1.52549
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 37.5648 2.07734
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −17.3607 −0.954229 −0.477115 0.878841i \(-0.658317\pi\)
−0.477115 + 0.878841i \(0.658317\pi\)
\(332\) 0 0
\(333\) 9.47214 0.519070
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −17.1246 −0.932837 −0.466419 0.884564i \(-0.654456\pi\)
−0.466419 + 0.884564i \(0.654456\pi\)
\(338\) 0 0
\(339\) −31.4953 −1.71059
\(340\) 0 0
\(341\) 45.3035 2.45332
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 25.3607 1.36143 0.680716 0.732547i \(-0.261669\pi\)
0.680716 + 0.732547i \(0.261669\pi\)
\(348\) 0 0
\(349\) 34.9427 1.87044 0.935219 0.354069i \(-0.115202\pi\)
0.935219 + 0.354069i \(0.115202\pi\)
\(350\) 0 0
\(351\) 1.52786 0.0815513
\(352\) 0 0
\(353\) 11.7751 0.626724 0.313362 0.949634i \(-0.398545\pi\)
0.313362 + 0.949634i \(0.398545\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −29.0689 −1.53420 −0.767099 0.641529i \(-0.778300\pi\)
−0.767099 + 0.641529i \(0.778300\pi\)
\(360\) 0 0
\(361\) 16.8885 0.888871
\(362\) 0 0
\(363\) −43.3491 −2.27524
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 5.78437 0.301942 0.150971 0.988538i \(-0.451760\pi\)
0.150971 + 0.988538i \(0.451760\pi\)
\(368\) 0 0
\(369\) −11.4412 −0.595607
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 30.1246 1.55979 0.779897 0.625908i \(-0.215272\pi\)
0.779897 + 0.625908i \(0.215272\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.206331 0.0106266
\(378\) 0 0
\(379\) 10.1246 0.520066 0.260033 0.965600i \(-0.416266\pi\)
0.260033 + 0.965600i \(0.416266\pi\)
\(380\) 0 0
\(381\) 25.5834 1.31068
\(382\) 0 0
\(383\) −21.5958 −1.10349 −0.551746 0.834012i \(-0.686038\pi\)
−0.551746 + 0.834012i \(0.686038\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 8.41641 0.427830
\(388\) 0 0
\(389\) −3.18034 −0.161250 −0.0806248 0.996745i \(-0.525692\pi\)
−0.0806248 + 0.996745i \(0.525692\pi\)
\(390\) 0 0
\(391\) 15.8902 0.803602
\(392\) 0 0
\(393\) −4.94427 −0.249406
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −7.73877 −0.388398 −0.194199 0.980962i \(-0.562211\pi\)
−0.194199 + 0.980962i \(0.562211\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0.708204 0.0353660 0.0176830 0.999844i \(-0.494371\pi\)
0.0176830 + 0.999844i \(0.494371\pi\)
\(402\) 0 0
\(403\) −7.23607 −0.360454
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −23.1803 −1.14901
\(408\) 0 0
\(409\) −9.89949 −0.489499 −0.244749 0.969586i \(-0.578706\pi\)
−0.244749 + 0.969586i \(0.578706\pi\)
\(410\) 0 0
\(411\) −22.8825 −1.12871
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 23.7082 1.16100
\(418\) 0 0
\(419\) −22.4211 −1.09534 −0.547671 0.836694i \(-0.684485\pi\)
−0.547671 + 0.836694i \(0.684485\pi\)
\(420\) 0 0
\(421\) 30.5967 1.49119 0.745597 0.666397i \(-0.232164\pi\)
0.745597 + 0.666397i \(0.232164\pi\)
\(422\) 0 0
\(423\) −10.9799 −0.533859
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 10.9443 0.528394
\(430\) 0 0
\(431\) 14.6525 0.705785 0.352892 0.935664i \(-0.385198\pi\)
0.352892 + 0.935664i \(0.385198\pi\)
\(432\) 0 0
\(433\) −2.41577 −0.116094 −0.0580471 0.998314i \(-0.518487\pi\)
−0.0580471 + 0.998314i \(0.518487\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 20.8005 0.995025
\(438\) 0 0
\(439\) 23.7565 1.13384 0.566918 0.823774i \(-0.308136\pi\)
0.566918 + 0.823774i \(0.308136\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 39.1246 1.85887 0.929433 0.368990i \(-0.120296\pi\)
0.929433 + 0.368990i \(0.120296\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −15.3500 −0.726031
\(448\) 0 0
\(449\) 9.76393 0.460788 0.230394 0.973097i \(-0.425998\pi\)
0.230394 + 0.973097i \(0.425998\pi\)
\(450\) 0 0
\(451\) 27.9991 1.31843
\(452\) 0 0
\(453\) −18.8461 −0.885469
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −25.6525 −1.19997 −0.599986 0.800010i \(-0.704827\pi\)
−0.599986 + 0.800010i \(0.704827\pi\)
\(458\) 0 0
\(459\) −8.00000 −0.373408
\(460\) 0 0
\(461\) 17.0193 0.792666 0.396333 0.918107i \(-0.370282\pi\)
0.396333 + 0.918107i \(0.370282\pi\)
\(462\) 0 0
\(463\) 13.4164 0.623513 0.311757 0.950162i \(-0.399083\pi\)
0.311757 + 0.950162i \(0.399083\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 17.5595 0.812555 0.406277 0.913750i \(-0.366827\pi\)
0.406277 + 0.913750i \(0.366827\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 20.6525 0.951616
\(472\) 0 0
\(473\) −20.5967 −0.947039
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 26.1803 1.19872
\(478\) 0 0
\(479\) 27.4102 1.25241 0.626203 0.779660i \(-0.284608\pi\)
0.626203 + 0.779660i \(0.284608\pi\)
\(480\) 0 0
\(481\) 3.70246 0.168818
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −31.4721 −1.42614 −0.713069 0.701094i \(-0.752696\pi\)
−0.713069 + 0.701094i \(0.752696\pi\)
\(488\) 0 0
\(489\) 4.98915 0.225617
\(490\) 0 0
\(491\) 1.76393 0.0796051 0.0398026 0.999208i \(-0.487327\pi\)
0.0398026 + 0.999208i \(0.487327\pi\)
\(492\) 0 0
\(493\) −1.08036 −0.0486571
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −26.9443 −1.20619 −0.603096 0.797669i \(-0.706066\pi\)
−0.603096 + 0.797669i \(0.706066\pi\)
\(500\) 0 0
\(501\) 9.41641 0.420694
\(502\) 0 0
\(503\) −12.3153 −0.549110 −0.274555 0.961571i \(-0.588531\pi\)
−0.274555 + 0.961571i \(0.588531\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 27.9991 1.24348
\(508\) 0 0
\(509\) −15.0162 −0.665580 −0.332790 0.943001i \(-0.607990\pi\)
−0.332790 + 0.943001i \(0.607990\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −10.4721 −0.462356
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 26.8701 1.18174
\(518\) 0 0
\(519\) −42.0689 −1.84662
\(520\) 0 0
\(521\) −34.5300 −1.51279 −0.756394 0.654117i \(-0.773041\pi\)
−0.756394 + 0.654117i \(0.773041\pi\)
\(522\) 0 0
\(523\) −3.90879 −0.170919 −0.0854597 0.996342i \(-0.527236\pi\)
−0.0854597 + 0.996342i \(0.527236\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 37.8885 1.65045
\(528\) 0 0
\(529\) −10.9443 −0.475838
\(530\) 0 0
\(531\) 4.37016 0.189649
\(532\) 0 0
\(533\) −4.47214 −0.193710
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −3.90879 −0.168677
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −10.7082 −0.460382 −0.230191 0.973146i \(-0.573935\pi\)
−0.230191 + 0.973146i \(0.573935\pi\)
\(542\) 0 0
\(543\) −8.29180 −0.355835
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −3.29180 −0.140747 −0.0703735 0.997521i \(-0.522419\pi\)
−0.0703735 + 0.997521i \(0.522419\pi\)
\(548\) 0 0
\(549\) −16.8430 −0.718844
\(550\) 0 0
\(551\) −1.41421 −0.0602475
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 14.3475 0.607924 0.303962 0.952684i \(-0.401690\pi\)
0.303962 + 0.952684i \(0.401690\pi\)
\(558\) 0 0
\(559\) 3.28980 0.139144
\(560\) 0 0
\(561\) −57.3050 −2.41942
\(562\) 0 0
\(563\) 41.6799 1.75660 0.878299 0.478112i \(-0.158679\pi\)
0.878299 + 0.478112i \(0.158679\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 23.9443 1.00380 0.501898 0.864927i \(-0.332635\pi\)
0.501898 + 0.864927i \(0.332635\pi\)
\(570\) 0 0
\(571\) 4.34752 0.181938 0.0909691 0.995854i \(-0.471004\pi\)
0.0909691 + 0.995854i \(0.471004\pi\)
\(572\) 0 0
\(573\) 27.8716 1.16435
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −39.5192 −1.64520 −0.822602 0.568617i \(-0.807479\pi\)
−0.822602 + 0.568617i \(0.807479\pi\)
\(578\) 0 0
\(579\) 35.8167 1.48849
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −64.0689 −2.65346
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −36.8971 −1.52291 −0.761453 0.648221i \(-0.775513\pi\)
−0.761453 + 0.648221i \(0.775513\pi\)
\(588\) 0 0
\(589\) 49.5967 2.04360
\(590\) 0 0
\(591\) −44.5570 −1.83283
\(592\) 0 0
\(593\) 30.5424 1.25423 0.627113 0.778928i \(-0.284236\pi\)
0.627113 + 0.778928i \(0.284236\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −49.5967 −2.02986
\(598\) 0 0
\(599\) 8.52786 0.348439 0.174220 0.984707i \(-0.444260\pi\)
0.174220 + 0.984707i \(0.444260\pi\)
\(600\) 0 0
\(601\) −32.4481 −1.32359 −0.661793 0.749687i \(-0.730204\pi\)
−0.661793 + 0.749687i \(0.730204\pi\)
\(602\) 0 0
\(603\) −31.1803 −1.26976
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −5.03786 −0.204480 −0.102240 0.994760i \(-0.532601\pi\)
−0.102240 + 0.994760i \(0.532601\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4.29180 −0.173627
\(612\) 0 0
\(613\) 26.8885 1.08602 0.543009 0.839727i \(-0.317285\pi\)
0.543009 + 0.839727i \(0.317285\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −15.3607 −0.618398 −0.309199 0.950997i \(-0.600061\pi\)
−0.309199 + 0.950997i \(0.600061\pi\)
\(618\) 0 0
\(619\) 26.1723 1.05195 0.525976 0.850500i \(-0.323700\pi\)
0.525976 + 0.850500i \(0.323700\pi\)
\(620\) 0 0
\(621\) −6.06952 −0.243561
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −75.0132 −2.99574
\(628\) 0 0
\(629\) −19.3863 −0.772984
\(630\) 0 0
\(631\) −1.00000 −0.0398094 −0.0199047 0.999802i \(-0.506336\pi\)
−0.0199047 + 0.999802i \(0.506336\pi\)
\(632\) 0 0
\(633\) −21.8021 −0.866555
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 37.3607 1.47797
\(640\) 0 0
\(641\) −39.3607 −1.55465 −0.777327 0.629097i \(-0.783425\pi\)
−0.777327 + 0.629097i \(0.783425\pi\)
\(642\) 0 0
\(643\) 26.3786 1.04027 0.520135 0.854084i \(-0.325882\pi\)
0.520135 + 0.854084i \(0.325882\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12.4729 0.490360 0.245180 0.969478i \(-0.421153\pi\)
0.245180 + 0.969478i \(0.421153\pi\)
\(648\) 0 0
\(649\) −10.6947 −0.419804
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −35.3050 −1.38159 −0.690795 0.723051i \(-0.742739\pi\)
−0.690795 + 0.723051i \(0.742739\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 16.8430 0.657110
\(658\) 0 0
\(659\) 16.4721 0.641663 0.320832 0.947136i \(-0.396038\pi\)
0.320832 + 0.947136i \(0.396038\pi\)
\(660\) 0 0
\(661\) 44.0957 1.71512 0.857561 0.514382i \(-0.171979\pi\)
0.857561 + 0.514382i \(0.171979\pi\)
\(662\) 0 0
\(663\) 9.15298 0.355472
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.819660 −0.0317374
\(668\) 0 0
\(669\) 27.1246 1.04870
\(670\) 0 0
\(671\) 41.2185 1.59122
\(672\) 0 0
\(673\) −8.29180 −0.319625 −0.159813 0.987147i \(-0.551089\pi\)
−0.159813 + 0.987147i \(0.551089\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −30.7788 −1.18293 −0.591464 0.806332i \(-0.701450\pi\)
−0.591464 + 0.806332i \(0.701450\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −14.6525 −0.561484
\(682\) 0 0
\(683\) 9.47214 0.362441 0.181221 0.983442i \(-0.441995\pi\)
0.181221 + 0.983442i \(0.441995\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −12.7639 −0.486974
\(688\) 0 0
\(689\) 10.2333 0.389859
\(690\) 0 0
\(691\) −27.0764 −1.03003 −0.515017 0.857180i \(-0.672214\pi\)
−0.515017 + 0.857180i \(0.672214\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 23.4164 0.886960
\(698\) 0 0
\(699\) −24.0903 −0.911180
\(700\) 0 0
\(701\) 34.2492 1.29358 0.646788 0.762670i \(-0.276112\pi\)
0.646788 + 0.762670i \(0.276112\pi\)
\(702\) 0 0
\(703\) −25.3770 −0.957113
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −15.8885 −0.596707 −0.298353 0.954455i \(-0.596437\pi\)
−0.298353 + 0.954455i \(0.596437\pi\)
\(710\) 0 0
\(711\) −25.6525 −0.962043
\(712\) 0 0
\(713\) 28.7456 1.07653
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −19.7990 −0.739407
\(718\) 0 0
\(719\) −23.6777 −0.883028 −0.441514 0.897254i \(-0.645559\pi\)
−0.441514 + 0.897254i \(0.645559\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −3.23607 −0.120351
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 37.9473 1.40739 0.703694 0.710503i \(-0.251532\pi\)
0.703694 + 0.710503i \(0.251532\pi\)
\(728\) 0 0
\(729\) −11.9443 −0.442380
\(730\) 0 0
\(731\) −17.2256 −0.637112
\(732\) 0 0
\(733\) −19.1313 −0.706630 −0.353315 0.935504i \(-0.614946\pi\)
−0.353315 + 0.935504i \(0.614946\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 76.3050 2.81073
\(738\) 0 0
\(739\) −18.0557 −0.664191 −0.332095 0.943246i \(-0.607756\pi\)
−0.332095 + 0.943246i \(0.607756\pi\)
\(740\) 0 0
\(741\) 11.9814 0.440148
\(742\) 0 0
\(743\) −46.1803 −1.69419 −0.847096 0.531440i \(-0.821651\pi\)
−0.847096 + 0.531440i \(0.821651\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −27.2526 −0.997121
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 4.94427 0.180419 0.0902095 0.995923i \(-0.471246\pi\)
0.0902095 + 0.995923i \(0.471246\pi\)
\(752\) 0 0
\(753\) 4.00000 0.145768
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 49.7214 1.80715 0.903577 0.428426i \(-0.140932\pi\)
0.903577 + 0.428426i \(0.140932\pi\)
\(758\) 0 0
\(759\) −43.4767 −1.57810
\(760\) 0 0
\(761\) −49.9287 −1.80992 −0.904958 0.425501i \(-0.860098\pi\)
−0.904958 + 0.425501i \(0.860098\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.70820 0.0616797
\(768\) 0 0
\(769\) 16.6854 0.601692 0.300846 0.953673i \(-0.402731\pi\)
0.300846 + 0.953673i \(0.402731\pi\)
\(770\) 0 0
\(771\) 18.9443 0.682261
\(772\) 0 0
\(773\) 6.94355 0.249742 0.124871 0.992173i \(-0.460148\pi\)
0.124871 + 0.992173i \(0.460148\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 30.6525 1.09824
\(780\) 0 0
\(781\) −91.4296 −3.27161
\(782\) 0 0
\(783\) 0.412662 0.0147473
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −38.4875 −1.37193 −0.685966 0.727634i \(-0.740620\pi\)
−0.685966 + 0.727634i \(0.740620\pi\)
\(788\) 0 0
\(789\) 24.5030 0.872330
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −6.58359 −0.233790
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −14.3972 −0.509974 −0.254987 0.966944i \(-0.582071\pi\)
−0.254987 + 0.966944i \(0.582071\pi\)
\(798\) 0 0
\(799\) 22.4721 0.795007
\(800\) 0 0
\(801\) −13.1105 −0.463236
\(802\) 0 0
\(803\) −41.2185 −1.45457
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −73.7771 −2.59708
\(808\) 0 0
\(809\) 11.8754 0.417516 0.208758 0.977967i \(-0.433058\pi\)
0.208758 + 0.977967i \(0.433058\pi\)
\(810\) 0 0
\(811\) −10.1545 −0.356574 −0.178287 0.983979i \(-0.557056\pi\)
−0.178287 + 0.983979i \(0.557056\pi\)
\(812\) 0 0
\(813\) −56.8328 −1.99321
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −22.5486 −0.788876
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −19.5279 −0.681527 −0.340764 0.940149i \(-0.610686\pi\)
−0.340764 + 0.940149i \(0.610686\pi\)
\(822\) 0 0
\(823\) −16.0557 −0.559667 −0.279834 0.960048i \(-0.590279\pi\)
−0.279834 + 0.960048i \(0.590279\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −47.6525 −1.65704 −0.828519 0.559960i \(-0.810816\pi\)
−0.828519 + 0.559960i \(0.810816\pi\)
\(828\) 0 0
\(829\) −43.3491 −1.50558 −0.752789 0.658262i \(-0.771292\pi\)
−0.752789 + 0.658262i \(0.771292\pi\)
\(830\) 0 0
\(831\) −47.9256 −1.66252
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −14.4721 −0.500230
\(838\) 0 0
\(839\) −23.5803 −0.814081 −0.407040 0.913410i \(-0.633439\pi\)
−0.407040 + 0.913410i \(0.633439\pi\)
\(840\) 0 0
\(841\) −28.9443 −0.998078
\(842\) 0 0
\(843\) 55.2030 1.90129
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 24.1803 0.829867
\(850\) 0 0
\(851\) −14.7082 −0.504191
\(852\) 0 0
\(853\) −0.255039 −0.00873237 −0.00436619 0.999990i \(-0.501390\pi\)
−0.00436619 + 0.999990i \(0.501390\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −6.03941 −0.206302 −0.103151 0.994666i \(-0.532893\pi\)
−0.103151 + 0.994666i \(0.532893\pi\)
\(858\) 0 0
\(859\) −10.4096 −0.355170 −0.177585 0.984105i \(-0.556828\pi\)
−0.177585 + 0.984105i \(0.556828\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −9.87539 −0.336162 −0.168081 0.985773i \(-0.553757\pi\)
−0.168081 + 0.985773i \(0.553757\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −9.02546 −0.306521
\(868\) 0 0
\(869\) 62.7771 2.12957
\(870\) 0 0
\(871\) −12.1877 −0.412966
\(872\) 0 0
\(873\) −36.5632 −1.23748
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 44.4296 1.50028 0.750140 0.661279i \(-0.229986\pi\)
0.750140 + 0.661279i \(0.229986\pi\)
\(878\) 0 0
\(879\) −45.4164 −1.53186
\(880\) 0 0
\(881\) −28.7456 −0.968465 −0.484233 0.874939i \(-0.660901\pi\)
−0.484233 + 0.874939i \(0.660901\pi\)
\(882\) 0 0
\(883\) −6.05573 −0.203791 −0.101896 0.994795i \(-0.532491\pi\)
−0.101896 + 0.994795i \(0.532491\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −48.4658 −1.62732 −0.813661 0.581339i \(-0.802529\pi\)
−0.813661 + 0.581339i \(0.802529\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 58.5967 1.96306
\(892\) 0 0
\(893\) 29.4164 0.984383
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 6.94427 0.231862
\(898\) 0 0
\(899\) −1.95440 −0.0651827
\(900\) 0 0
\(901\) −53.5825 −1.78509
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 27.7771 0.922323 0.461162 0.887316i \(-0.347433\pi\)
0.461162 + 0.887316i \(0.347433\pi\)
\(908\) 0 0
\(909\) −7.53244 −0.249835
\(910\) 0 0
\(911\) −7.11146 −0.235613 −0.117807 0.993037i \(-0.537586\pi\)
−0.117807 + 0.993037i \(0.537586\pi\)
\(912\) 0 0
\(913\) 66.6930 2.20722
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 18.7082 0.617127 0.308563 0.951204i \(-0.400152\pi\)
0.308563 + 0.951204i \(0.400152\pi\)
\(920\) 0 0
\(921\) 42.8328 1.41139
\(922\) 0 0
\(923\) 14.6035 0.480680
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 41.1096 1.35022
\(928\) 0 0
\(929\) 27.9991 0.918622 0.459311 0.888276i \(-0.348096\pi\)
0.459311 + 0.888276i \(0.348096\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −21.5279 −0.704791
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 55.6157 1.81689 0.908443 0.418009i \(-0.137272\pi\)
0.908443 + 0.418009i \(0.137272\pi\)
\(938\) 0 0
\(939\) −8.18034 −0.266955
\(940\) 0 0
\(941\) 6.78593 0.221215 0.110607 0.993864i \(-0.464720\pi\)
0.110607 + 0.993864i \(0.464720\pi\)
\(942\) 0 0
\(943\) 17.7658 0.578534
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −15.7771 −0.512686 −0.256343 0.966586i \(-0.582518\pi\)
−0.256343 + 0.966586i \(0.582518\pi\)
\(948\) 0 0
\(949\) 6.58359 0.213712
\(950\) 0 0
\(951\) 0.952843 0.0308981
\(952\) 0 0
\(953\) 55.9017 1.81083 0.905417 0.424524i \(-0.139558\pi\)
0.905417 + 0.424524i \(0.139558\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 2.95595 0.0955522
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 37.5410 1.21100
\(962\) 0 0
\(963\) 27.8885 0.898696
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −4.58359 −0.147398 −0.0736992 0.997281i \(-0.523480\pi\)
−0.0736992 + 0.997281i \(0.523480\pi\)
\(968\) 0 0
\(969\) −62.7355 −2.01535
\(970\) 0 0
\(971\) −12.4729 −0.400274 −0.200137 0.979768i \(-0.564139\pi\)
−0.200137 + 0.979768i \(0.564139\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −6.59675 −0.211049 −0.105524 0.994417i \(-0.533652\pi\)
−0.105524 + 0.994417i \(0.533652\pi\)
\(978\) 0 0
\(979\) 32.0841 1.02541
\(980\) 0 0
\(981\) −36.7082 −1.17200
\(982\) 0 0
\(983\) 42.4751 1.35475 0.677373 0.735640i \(-0.263118\pi\)
0.677373 + 0.735640i \(0.263118\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −13.0689 −0.415566
\(990\) 0 0
\(991\) 4.34752 0.138104 0.0690518 0.997613i \(-0.478003\pi\)
0.0690518 + 0.997613i \(0.478003\pi\)
\(992\) 0 0
\(993\) 39.7255 1.26065
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −9.23179 −0.292374 −0.146187 0.989257i \(-0.546700\pi\)
−0.146187 + 0.989257i \(0.546700\pi\)
\(998\) 0 0
\(999\) 7.40492 0.234281
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4900.2.a.bi.1.1 yes 4
5.2 odd 4 4900.2.e.u.2549.8 8
5.3 odd 4 4900.2.e.u.2549.2 8
5.4 even 2 4900.2.a.bg.1.4 yes 4
7.6 odd 2 inner 4900.2.a.bi.1.4 yes 4
35.13 even 4 4900.2.e.u.2549.7 8
35.27 even 4 4900.2.e.u.2549.1 8
35.34 odd 2 4900.2.a.bg.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4900.2.a.bg.1.1 4 35.34 odd 2
4900.2.a.bg.1.4 yes 4 5.4 even 2
4900.2.a.bi.1.1 yes 4 1.1 even 1 trivial
4900.2.a.bi.1.4 yes 4 7.6 odd 2 inner
4900.2.e.u.2549.1 8 35.27 even 4
4900.2.e.u.2549.2 8 5.3 odd 4
4900.2.e.u.2549.7 8 35.13 even 4
4900.2.e.u.2549.8 8 5.2 odd 4